Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity

We consider the nonlinear Schrödinger equation: (1) $${{i\partial u} \mathord{\left/ {\vphantom {{i\partial u} {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}} = - \Delta u - \left| u \right|^{{4 \mathord{\left/ {\vphantom {4 N}} \right. \kern-\nulldelimiterspace} N}} uandu\left( {0,.} \right) = \varphi \left( . \right),$$ whereu:[0,T)×? ^N →?. For any given pointsx ₁,x ₂,...,x _k in ? ^N , we construct a solution of Eq. (1),u(t), which blows up in a finite timeT at exactlyx ₁,x ₂,...,x _k . In addition, we describe the precise behavior of the solutionu(t) whent→T, at the blow-up points {x ₁,x ₂,...,x _k } and in ? ^N ?{x ₁,x ₂,...,x _k }.     

Iron-57 Mössbauer spectroscopic studies of materials of composition Fe x NbTiP3O12: materials with low concentrations of iron and the effects of treatment in air

The⁵⁷Fe Mössbauer spectrum recorded from the material of composition Fe_0.25NbTiP₃O₁₂ shows the presence of Fe²⁺ in a distribution of approximately octahedral type I sites within the channels of the NbTiP₃O₁₂ structure. A comparison of the results with those recorded from the material Fe_0.33NbTiP₃O₁₂ demonstrates the existence of an upper limit to the occupation by the Fe²⁺ species of the type I sites. Lattice parameter measurements and⁵⁷Fe Mössbauer spectroscopy show that treatment of Fe_0.25NbTiP₃O₁₂ in air induces the migration of the incorporated iron from the channels to form macroscopic -Fe₂O₃.     

Purification and analysis of partially alkylated cyclodextrins by liquid and gas chromatography

Complex mixtures of partially alkylated cyclodextrins can be analyzed by both HPLC and high temperature capillary GC. Because of the limited efficiency of LC, suitable analytical and preparative separations can be achieved only with systems of carefully optimized selectivity. Using LC it has been possible to isolate and purify single cyclodextrin species from very complex mixtures of components which contain unreacted hydroxyl groups in addition to the alkoxy groups. Analysis of the reaction mixtures and of fractions taken from LC separations can be performed with advantage by high resolution capillary GC at high temperatures between 300 and 400 °C. The thermal stability of partially alkylated cyclodextrins in high temperature GC is considerably increased by trimethylsilylation of the free hydroxyl groups. Fast atom bombardment mass spectrometry and proton NMR were used to identify species isolated from the preparative LC separations.     

Precipitates originating from tungsten crucible parts in AlN bulk crystals grown by the PVT method

In order to evaluate the possible involvement of crucible materials in the growth of AlN bulk crystals grown by physical vapor transport, we applied growth conditions with a high vertical thermal gradient and hence high supersaturation of aluminum vapor. Under these conditions, precipitates formed causing diffuse grayish substructures at the initial growth interface and in the crystal body, decorating dislocations. Electron microscopy studies revealed that the precipitates are elongated, single‐phase particles with sizes of 50–500 nm of commensurate structure, oriented along the <110> direction. Chemical analysis of the precipitates showed tungsten as well as carbon and oxygen. The lattice parameters of the precipitates are in close agreement to hexagonal tungsten hemicarbide (W₂C). The possible transport from the tungsten parts and its conversion into tungsten hemicarbide precipitates is discussed. We thus conclude that the W₂C precipitates may contribute to the decoration of dislocations, even in growth with moderate thermal gradients.     

Phosphaniminato‐Acetato‐Cluster von Kupfer und Zink. Kristallstrukturen von [Cu4(NPEt3)2(O2CCH3)6] und [Zn4(NPEt3)2(O2CCH3)6]

Phosphoraneiminato Acetate Cluster of Copper and Zinc. Crystal Structures of [Cu₄(NPEt₃)₂(O₂CCH₃)₆] and [Zn₄(NPEt₃)₂(O₂CCH₃)₆] The anhydrous acetates of copper(II) and zinc react with the silylated phosphaneimine Me₃SiNPEt₃ in dichloromethane at 20 °C forming the mixed phosphoraneiminato acetate clusters [Cu₄(NPEt₃)₂(O₂CCH₃)₆] ( 1 ), which forms emerald crystals, and colourless [Zn₄(NPEt₃)₂ · (O₂CCH₃)₆] ( 2 ). In spite of analogous composition the structures of 1 and 2 are completely different. In the asymmetric unit of 1 three copper atoms of an almost isosceles triangle are linked via two nitrogen atoms of the NPEt₃^– groups to form a trigonal bipyramidal aggregate. One of these three copper atoms is chelated by an acetate group, another one is connected with the fourth copper atom via three μ₂‐O₂C–CH₃ groups. The asymmetric units are associated via a μ₂‐O₂C–CH₃ group and a μ₃‐OC(O)CH₃ group at a time so that infinite chains result. In 2 two zinc atoms are linked via the nitrogen atoms of the two NPEt₃^– groups to form an almost centrosymmetric four‐membered ring. Both nitrogen atoms of the four‐membered ring are connected with another zinc atom each. These zinc atoms again are linked with the zinc atoms of the Zn₂N₂ four‐membered ring via two μ₂‐O₂C–CH₃ groups each and additionally coordinated with a terminal acetate ligand each.     

Gyroscope‐Like Molecules Consisting of PdX2/PtX2 Rotators within Three‐Spoke Dibridgehead Diphosphine Stators: Syntheses,Substitution Reactions,Structures, and Dynamic Properties

Threefold intramolecular ring‐closing metatheses of trans‐[MCl₂(P{(CH₂)_mCH?CH₂}₃)₂] are effected with Grubbs’ catalyst. Following hydrogenation catalyzed by [RhCl(PPh₃)₃], the title complexes trans‐[MCl₂(P((CH₂)_n)₃P )] (n=2m+2; M/n=Pt/14, 4 c ; Pt/16, 4 d ; Pt/18, 4 e ; Pd/14, 5 c ; Pd/18, 5 e ) and sometimes isomers partly derived from intraligand metathesis, trans‐[MCl₂{P(CH₂)_n(CH₂)_n}P (CH₂)_n)] ( 4′c–e , 5′e ), are isolated. These react with LiBr, NaI, and KCN to give the corresponding MBr₂, MI₂, and M(CN)₂ species (58–99 %). ¹³C NMR data show that the MX₂ moieties rapidly rotate within the diphosphine cage on the NMR timescale, even at ?120 °C. The reaction of 4 c and KSCN gives separable Pt(NCS)₂ and Pt(NCS)(SCN) adducts ( 13 c , 28 %; 14 c , 20 %), and those of 4 c , e and Ph₂Zn give PtPh₂ species ( 15 c , 61 %; 15 e , 90 %). ¹³C NMR spectra of 13 c – 15 c show two sets of CH₂ signals (ca. 2:1 intensity ratios), indicating that MX₂ rotation is no longer rapid. Reactions of 4 c or 4′c and excess NaC?CH afford the free diphosphines P{(CH₂)₁₄}₃P (91 %) and (CH₂)₁₄P (CH₂)₁₄P(C H₂)₁₄ (90 %). The latter has been crystallographically characterized as a bis(BH₃) adduct. The crystal structures of eight complexes with P(CH₂)₁₄P linkages (PtCl₂, PtBr₂, PtI₂, Pt(NCS)₂, PtPh₂, PdCl₂, PdBr₂, PdI₂) and 15 e have been determined, and intramolecular distances analyzed with respect to MX₂ rotation. The conformations of the (CH₂)₁₄ moieties and features of the crystal lattices are also discussed.     

A new application of scanning electrochemical microscopy for the label-free interrogation of antibody-antigen interactions

Within this work we present a ‘proof of principle’ study for the use of scanning electrochemical microscopy (SECM) to detect and image biomolecular interactions in a label-free assay as a potential alternative to current fluorescence techniques. Screen-printed carbon electrodes were used as the substrate for the deposition of a dotted array, where the dots consist of biotinylated polyethyleneimine. These were then further derivatised, first with neutravidin and then with a biotinylated antibody to the protein neuron specific enolase (NSE). SECM using a ferrocene carboxylic acid mediator showed clear differences between the array and the surrounding unmodified carbon. Imaging of the arrays before and following exposure to various concentrations of the antigen showed clear evidence for specific binding of the NSE antigen to the antibody derivatised dots. Non-specific binding was quantified. Control experiments with other proteins showed only non-specific binding across the whole of the substrate, thereby confirming that specific binding does occur between the antibody and antigen at the surface of the dots. Binding of the antigen was accompanied by a measured increase in current response, which may be explained in terms of protein electrostatic interaction and hydrophobic interactions to the mediator, thereby increasing the localised mediator flux. A calibration curve was obtained between 500 fg mL⁻¹ to 200 pg mL⁻¹ NSE which demonstrated a logarithmic relationship between the current change upon binding and antigen concentration without the need for any labelling of the substrate.     

DEKOIS: demanding evaluation kits for objective in silico screening--a versatile tool for benchmarking docking programs and scoring functions

For widely applied in silico screening techniques success depends on the rational selection of an appropriate method. We herein present a fast, versatile, and robust method to construct demanding evaluation kits for objective in silico screening (DEKOIS). This automated process enables creating tailor-made decoy sets for any given sets of bioactives. It facilitates a target-dependent validation of docking algorithms and scoring functions helping to save time and resources. We have developed metrics for assessing and improving decoy set quality and employ them to investigate how decoy embedding affects docking. We demonstrate that screening performance is target-dependent and can be impaired by latent actives in the decoy set (LADS) or enhanced by poor decoy embedding. The presented method allows extending and complementing the collection of publicly available high quality decoy sets toward new target space. All present and future DEKOIS data sets will be made accessible at www.dekois.com.     

Helical growth of semiconducting columnar dye assemblies based on chiral perylene bisimides

A perylene bisimide derivative bearing two phenyl substituents with chiral solubilizing alkyl chains at the imide N atoms has been synthesized, and its self-assembly properties in solution and condensed phase have been investigated. Temperature-dependent CD spectra revealed the coexistence of two different kinds of chiral aggregates, differing in size and handedness. The chiral side chains effect a higher order within the self-assemblies, resulting in an increased charge-carrier mobility in the columnar liquid crystalline mesophase. [structure: see text]     

Molecular assemblies of perylene bisimide dyes in water

Perylene bisimides are among the most valuable functional dyes and have numerous potential applications. As a result of their chemical robustness, photostability, and outstanding optical and electronic properties, these dyes have been applied as pigments, fluorescence sensors, and n‐semiconductors in organic electronics and photovoltaics. Moreover, the extended quadrupolar π system of this class of dyes has facilitated the construction of numerous supramolecular architectures with fascinating photophysical properties. However, the supramolecular approach to the formation of perylene bisimide aggregates has been restricted mostly to organic media. Pleasingly, considerable progress has been made in the last few years in developing water‐soluble perylene bisimides and their application in aqueous media. This Review provides an up‐to‐date overview on the self‐assembly of perylene bisimides through π–π interactions in aqueous media. Synthetic strategies for the preparation of water‐soluble perylene bisimides and the influence of water on the π–π stacking of perylene bisimides as well as the resulting applications are discussed.